A wavelet algorithm for the solution of a singular integral equation over a smooth two-dimensional manifold

DOI10.1216/jiea/1181074248zbMath0923.65082OpenAlexW2008301115MaRDI QIDQ1286348

Andreas Rathsfeld

Publication date: 17 October 1999

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/jie/VOL10-4/CONT10-4/CONT10-4.html

zbMATH Keywords

complexitysingular integral equationsboundary integral equationerror boundcollocationLaplace's equationwavelet algorithmsquadrature algorithmsbilinear trial functionsMolodensky problem

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Boundary element methods for boundary value problems involving PDEs (65N38)

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Hybrid collocation methods for Fredholm integral equations with weakly singular kernels ⋮ Fast collocation methods for high-dimensional weakly singular integral equations ⋮ Numerical methods for Fredholm integral equations with singular right-hand sides ⋮ A wavelet algorithm for the boundary element solution of a geodetic boundary value problem ⋮ A fast wavelet collocation method for integral equations on polygons ⋮ On a quadrature algorithm for the piecewise linear wavelet collocation applied to boundary integral equations

Cites Work

• Multilevel matrix multiplication and fast solution of integral equations
• Rapid solution of integral equations of classical potential theory
• On the fast matrix multiplication in the boundary element method by panel clustering
• A spline collocation method for multidimensional strongly elliptic pseudodifferential operators of order zero
• Multilevel preconditioning
• Spline approximation methods for multidimensional periodic pseudodifferential equations
• Wavelets on the interval and fast wavelet transforms
• Wavelet approximation methods for pseudodifferential equations. I: Stability and convergence
• Wavelet approximation methods for pseudodifferential equations. II: Matrix compression and fast solution
• A wavelet algorithm for the solution of the double layer potential equation over polygonal boundaries
• A wavelet algorithm for the boundary element solution of a geodetic boundary value problem
• Wavelet approximations for first kind boundary integral equations on polygons
• Fast wavelet transforms and numerical algorithms I
• An Analysis of Quadrature Errors in Second-Kind Boundary Integral Methods
• Error Bounds for Gaussian Quadrature and Weighted-$L^1$ Polynomial Approximation
• Ten Lectures on Wavelets
• Biorthogonal bases of compactly supported wavelets
• Fast Multiresolution Algorithms for Matrix-Vector Multiplication
• A fast algorithm for particle simulations
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